document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198404>Question 1198404</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In hw many ways can three items be selected from a group of six items. Use letters A B C D E and F to identity the items and list each of the different combination of three items </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831996 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831996\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are 6 choices for the first slot, then 6-1 = 5 choices for the second slot, and finally 5-1 = 4 choices for the third slot.\r<BR>\n" );
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document.write( "If order mattered, then we'd have 6*5*4 = 30*4 = 120 different permutations, and this would be the final answer.\r<BR>\n" );
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document.write( "But order doesn't matter. <BR>\n" );
document.write( "The group {A,B,C} is the same as something like {B,A,C}. <BR>\n" );
document.write( "The order doesn't matter when considering the group overall.\r<BR>\n" );
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document.write( "There are 3*2*1 = 6 ways to rearrange any given group of 3 items. <BR>\n" );
document.write( "This tells us that the previous figure of 120 is too large by a factor of 6.\r<BR>\n" );
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document.write( "Divide by 6 to correct for this over-counting: 120/6 = <font color=red>20</font><BR>\n" );
document.write( "Therefore, we have <font color=red>20</font> different groups of three letters chosen from a pool of six.\r<BR>\n" );
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document.write( "Alternatively you can use the nCr combination formula to get this answer. <BR>\n" );
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document.write( "Use n = 6 and r = 3. \r<BR>\n" );
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document.write( "Another alternative is to use Pascal's Triangle. <BR>\n" );
document.write( "Look at the row that starts with 1,6,... and you're looking for the item in the fourth slot. <BR>\n" );
document.write( "This is because the 'r' value starts counting at r = 0 rather than r = 1.\r<BR>\n" );
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document.write( "Answer: <font color=red>20</font><BR>\n" );
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